Abstract:
Two-dimensional unsteady stagnation-point flow of viscoelastic fluids is studied assuming that the fluid obeys the upper-convected Maxwell (UCM) model. The solutions of governing equations are found in assumptions that components of extra stress tensor are polynomials of spatial variable along solid wall.
A class of solutions for unsteady flow in the neighbourhood
of a front or rear stagnation point on a plane boundary is considered, and a
range of possible behaviour is revealed, depending
on an initial stage (initial data) and on whether the pressure gradient
is accelerating or decelerating function of time.
The velocity and stress tensor's components profiles are obtained by
numerical integration the system of nonlinear ordinary differential equation.
The solutions of equations exhibit finite-time singularities depending
on the initial data and the type of pressure gradient dependence on time.
Citation:
N. P. Moshkin, “Unsteady flow of Maxwell viscoelastic fluid near a critical point
with countercurrent at the initial moment”, Sib. Zh. Ind. Mat., 25:1 (2022), 92–104
\Bibitem{Mos22}
\by N.~P.~Moshkin
\paper Unsteady flow of Maxwell viscoelastic fluid near a critical point
with countercurrent at the initial moment
\jour Sib. Zh. Ind. Mat.
\yr 2022
\vol 25
\issue 1
\pages 92--104
\mathnet{http://mi.mathnet.ru/sjim1164}
\crossref{https://doi.org/10.33048/SIBJIM.2022.25.107}
Linking options:
https://www.mathnet.ru/eng/sjim1164
https://www.mathnet.ru/eng/sjim/v25/i1/p92
This publication is cited in the following 1 articles:
C. Chittam, S.V. Meleshko, “General solution of the Maxwell equations for the stagnation point problem with cylindrical symmetry for all values of the parameter in the Johnson-Segalman derivative”, Communications in Nonlinear Science and Numerical Simulation, 142 (2025), 108527